NFL Commissioner Roger Goodell issued the initial suspensions, which also included a full-season ban for Saints head coach Sean Payton.
Lawsuits brought by Vilma and the NFL Players Association to challenge Goodell's handling of the case, including his decision in October to appoint Tagliabue as the arbitrator for the appeals, are pending in federal court in New Orleans.
On Thursday, U.S. District Judge Ginger Berrigan gave the parties until Monday to answer questions about whether the NFL's collective bargaining agreement prevents a commissioner from handing out discipline for legal contact, and whether the CBA's passages about detrimental conduct are "ambiguous, hence unenforceable."
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AP Sports Writer Brett Martel in New Orleans contributed to this report.